When a flower petal is 4.0 cm in front of a convex lens,the inverted image is half the height of the petal.What is the focal length of this lens?

Question

Quizplus · Accepted Answer

The image is half the height of the object, so the magnification is 1/2. The magnification equation is:m = -i/o = 1/2where m is the magnification, i is the image distance, and o is the object distance.We can rearrange this equation to solve for the image distance:i = -o/2We know that the object distance is 4.0 cm, so the image distance is:i = -4.0 cm / 2 = -2.0 cmThe focal length of a lens is the distance between the lens and the image when the object is at infinity. In this case, the object is not at infinity, but we can still use the thin lens equation to find the focal length:1/f = 1/o + 1/iwhere f is the focal length.We know that the object distance is 4.0 cm and the image distance is -2.0 cm, so the focal length is:1/f = 1/4.0 cm + 1/-2.0 cm = 1/2.0 cmf = 2.0 cmTherefore, the focal length of the lens is 2.0 cm.

When a Flower Petal Is 4